1. Field of the Invention
The present invention relates to a method of creating a predictive model for use in process proximity effect correction, a method of managing process steps, a method of manufacturing a semiconductor device, a method of manufacturing a photo mask, and a computer program product.
2. Description of the Related Art
In recent years, with miniaturization of LSI, a pattern on a photo mask (mask pattern), having a dimension below 1 μm, has been required. By the miniaturization of the mask pattern, phenomena in which a resist pattern cannot be formed as designed on a wafer in a lithography step, that is, optical proximity effects (OPE) become obvious.
To suppress an influence of the OPE, a technique of forming the resist pattern as designed by use of a corrected photo mask, that is, optical proximity correction (OPC) is performed. Introduction of the OPC makes it possible to suppress fluctuations of a critical dimension (CD) on the wafer, and even a finer pattern can be finished faithfully as designed on the wafer.
Moreover, in recent years, phenomena in which a mask pattern cannot be formed on the photo mask as designed in accordance with mask drawing data in a step of manufacturing a photo mask and in which a pattern cannot be formed on the wafer as designed in accordance with the resist pattern in a processing step, that is, so-called process proximity effects (PPE) have become obvious.
To suppress the influence of the PPE, a technique of correcting a conversion difference through steps including the photo mask manufacturing step to the processing step, that is, a process proximity correction (PPC) has been performed.
There is one type of the PPC in which a finally obtained dimension of the pattern on the wafer is directly predicted from the mask drawing data using a process proximity effect predictive model, a conversion difference between the mask drawing data and the pattern on the wafer is estimated, and the finally obtained dimension is corrected (Proc. SPIE Vol. 3677 pl. 722 to 733, Stirnimann et. al).
Moreover, there is another PPC in which each conversion difference between the steps is estimated using predictive models prepared for each of the photo mask manufacturing step, lithography step, and processing step, and the dimension is corrected for each step (Jpn. Pat. Appln. KOKAI Publication No. 11-102062).
The predictive models are used in these PPCs as described above. A method of creating the predictive model has a step of preparing the mask drawing data corresponding to a plurality of repetition patterns to acquire the finally obtained dimension of the pattern on the wafer corresponding to the mask drawing data by experiments and a step of determining non-determined parameters in the predictive model by fitting by use of the mask drawing data and the finally obtained dimension.
As the mask drawing data, for example, as shown in FIG. 9, data corresponding to a plurality of line & space patterns having different pitches (=P1 to P8) are prepared. A line width is constant (=W1).
FIG. 10 shows a relation between the pitches P1 to P8 obtained by a conventional predictive model and the CDs of the finished line & space patterns on the wafer. Here, the CD is a width of the line pattern on the wafer.
The pitch of the line & space pattern of FIG. 10, that is, a pitch of the line & space pattern for an experiment does not necessarily match that of an actually used line & space pattern. A CD value corresponding to a pitch other than the pitch of the line & space pattern for use in the experiment is obtained by extrapolation. However, it is difficult to verify precision of the CD value obtained by the extrapolation. Therefore, there occurs a case that a prediction precision in an actually required pitch drops.
Moreover, as a result of the drop of the prediction precision in the actually required pitch, it is difficult to set a target of an allowable fluctuation amount of a process in a case where the process is managed in consideration of the PPE in each step. That is, it is difficult to manage steps of manufacturing a semiconductor from a viewpoint of the PPE.